arXiv:2606. 06486v1 Announce Type: new Abstract: In this paper, we study regret minimization in repeated games with \emph{adaptive} opponents who can respond based on histories of play.
arXiv:2608. 09389v1 Announce Type: cross Abstract: This note aims to serve as an entry point to the literature on learning in games, a topic with significant theoretical appeal and a wide range of applications -- from machine learning and data science to economics and beyond.
arXiv:2607. 23333v1 Announce Type: cross Abstract: We revisit the regret loss framework introduced in Park et al.
arXiv:2609.22839v1 Announce Type: cross Abstract: Can simple learning rules keep their regret bounded in self-play? Recent work achieves constant regret bounds through modified regularization and hig...
arXiv:2606. 01382v1 Announce Type: cross Abstract: Preference alignment is central to improving large language models, but standard reward-based formulations can be restrictive when human preferences are cyclic, non-transitive, or otherwise not representable by a scalar reward.
arXiv:2610. 08745v1 Announce Type: new Abstract: We study linear bandits under exact sliding-window constraints, where every consecutive block of actions must belong to a prescribed feasible set.
arXiv:2510. 22819v3 Announce Type: replace Abstract: The convergence analysis of online learning algorithms is central to machine learning theory, where the last-iterate convergence is particularly important, as it captures the learner's actual decisions and describes the evolution of the learning process over time.
The paper introduces a new algorithm for a nonstationary bandit setting where actions influence both immediate rewards and the evolution of an unobserved latent linear state. By approximating the infinite‑memory reward process with a finite‑memory block‑level proxy and applying a UCB‑based block algorithm, the authors achieve a regret bound of “~O(√T)”, improving upon the previous “~O(T^{2/3})” guarantee. This represents the first such “~O(√T)” result for latent linear‑dynamics bandits with bilinear rewards and an open‑loop action‑sequence benchmark.
The paper presents the first adversarial linear bandit algorithm based on Follow-the-Perturbed-Leader (FTPL) that achieves √T regret over general convex action sets. It achieves a regret of ≥O(d^{5/4}√T) using only linear optimization oracles, and a near‑optimal ≥O(d√T) regret when an optimal‑design exploration distribution is available. The work improves on previous FTPL algorithms and generalizes earlier results for special action sets, offering a simpler and more computationally efficient approach that relies on adaptive perturbation distributions and a new analysis framework based on Fisher information.
The paper presents an uncoupled learning algorithm, higher-order optimism with discounting (HOOD), for arbitrary N-player normal form games with up to K actions per player. HOOD achieves an individual regret bound of O(N³ log² K) uniformly over the play horizon by combining a discounted (N+1)-th order predictor with entropic regularization over a lifted strategy space. This design mitigates large oscillations in play, addressing a key challenge in prior attempts to attain constant regret in general games.
The paper presents the first adversarial linear bandit algorithm based on Follow-the-Perturbed-Leader (FTPL) that achieves √T regret over general action sets. It attains a ≥O(d^{5/4}√T) regret using only linear optimization oracles, and a near‑optimal ≥O(d√T) regret when an optimal‑design exploration distribution is available. The authors introduce adaptive perturbation distributions—including Gaussian, random‑weighting, and elliptical perturbations—and develop a systematic analysis of the FTPL stability term via Fisher information, extending the FTPL framework beyond previous approaches.
The paper studies the trade‑off between maximizing rewards and accurately estimating current treatment effects in nonstationary multi‑armed bandits. For $K$‑armed bandits with H"older‑smooth mean rewards, the authors derive minimax bounds on expected dynamic regret under a high‑probability simultaneous coverage requirement for all current effects. They propose the TRACE algorithm, which achieves a regret–precision trade‑off that separates reward‑learning regret from the unavoidable cost of refreshing current‑effect estimates, and extend the method with an empirical‑Bernstein e‑process to adapt exploration while preserving worst‑case guarantees.